Question

What is the present age of Shilpa?
I. Shilpa's present age is five times of Rahul's present age.
II. Five years ago her age was twenty-five times of Rahul's age at that time.

• A. If the statement I alone is sufficient to answer the question.
• B. If the statement II alone is sufficient to answer the question.
• C. If the statements I and II together are sufficient to answer the question but neither statement alone is sufficient.
• D. If the statements I and II together are not sufficient to answer the question and additional data is required.

Hint:

When dealing with age-related problems, set up algebraic equations based on the given relationships and solve for the unknowns systematically.

Answer 1

The Correct Option is C

Let Shilpa's present age be \( S \) and Rahul's present age be \( R \). From condition I: \[ S = 5R \] From condition II: Five years ago, Shilpa's age was 25 times Rahul's age at that time. So, five years ago, Shilpa’s age was \( S - 5 \) and Rahul’s age was \( R - 5 \). The equation becomes: \[ S - 5 = 25(R - 5) \] Substitute \( S = 5R \) into this equation: \[ 5R - 5 = 25(R - 5) \] Simplifying: \[ 5R - 5 = 25R - 125 \] \[ 5R - 25R = -125 + 5 \] \[ -20R = -120 \] \[ R = 6 \] Now substitute \( R = 6 \) into \( S = 5R \): \[ S = 5 \times 6 = 30 \] Thus, Shilpa’s present age is \( \boxed{30} \). Therefore, the correct answer is \( \boxed{3} \).